This proposal is submitted in response to RFA: HL-11-013 to propose the Stanford University Blood and Marrow Transplant (BMT) Program as a Core Clinical Center for the Blood and Marrow Clinical Trials Network. The BMT Program at Stanford University performs ~250 adult transplant and ~ 20 pediatric transplants/ year including autologous and allogeneic procedures with matched related, mismatched related and matched unrelated donors. Both myeloablative and non-myeloablative transplants are performed for hematologic malignancies. The BMT Program at Stanford participates in clinical research as a single institution, consortia, regional oncology group and national trials and has been a leader in defining the role and optimizing transplantation for patients with hematologic malignancies. The Program has a highly experienced data management group and a GMP-certified stem cell processing laboratory. The Stanford BMT program is an active participant in current network activities and has performed at a high level as one of the charter Core Centers. Stanford has accrued 141 patients to date to 10 CTN trials and Stanford investigators have served as national Chairs on three network protocols and chaired two CTN committees. The protocol that is proposed aims to improve upon the strategy of T cell depletion in the allogeneic myeloablative HCT setting in patients with hematologic malignancies using matched related donors. We propose T cell add back after HCT simultaneously with infusion of naturally occurring regulatory T cells in pre-defined doses and ratios. The hypothesis is that such maneuvers will improve immune reconstitution and decrease relapse risk but with control of acute GVHD due to the suppressive mechanisms of the regulatory T cells. No post-HCT immunesuppression will be administered. The Stanford BMT Program is committed to continued participation in network trials as well as contributing concepts for consideration by the group. RELEVANCE (See instructions): The mission of this grant is to form a network of established stem cell transplant centers such as the Stanford Blood and Marrow Transplant Program to collaborate and conduct multicenter clinical trials. The common goal of these clinical trials is to cure cancers such as leukemia, lymphoma, myeloma and some non-malignant diseases such as sickle cell disease and aplastic anemia. Some of the clinical trials also aim to reduce the side effects and toxic effects of stem cell transplantation